The primary objective of this study is to determine the safety of intrathecal delivery of autologous mesenchymal stem cells (MSCs) to the cerebrospinal fluid (CSF) of patients with ALS using a dose-escalation study. The trial will include 25 adult, non-ventilator-dependent patients with clinically definite amyotrophic lateral sclerosis (ALS). Cells will be isolated from adipose tissue, expanded ex vivo and then, after ~8 weeks, intrathecal (IT) autologous delivery of MSCs will be performed. There will be 5 treatment groups of up to 5 patients each. Groups 1, 2, and 4 will receive a single dose of cells. Groups 3 and 5 will receive 2 doses of cells separated by 1 month. Groups will be completed sequentially so that patients will not be enrolled into the next treatment group until at least 3 patients in the preceding group have completed the treatment and 1 month of additional observation without significant toxicity. All patients will be followed on a regular basis until death or for a minimum of 2 years after completion of the final infusion. Initial clinical follow-up will be weekly with scheduled blood, CSF and magnetic resonance imaging (MRI) evaluations. After 1 month, patients will have clinical evaluations at 3 month intervals, or earlier if indicated by clinical status.